Marcin Wardyński
Tue, 9:45AM

import sklearn
import sklearn.datasets
import sklearn.ensemble
import numpy as np
import pandas as pd
import lime
import lime.lime_tabular
from __future__ import print_function
np.random.seed(1)

Numerical and Categorical features in the same dataset

We will analyse a dataset that has both numerical and categorical features. Here, the task is to predict whether a person makes over 50K dollars per year.

feature_names = ["Age", "Workclass", "fnlwgt", "Education", "Education-Num", "Marital Status", "Occupation", "Relationship", "Race", "Sex", 
                 "Capital Gain", "Capital Loss","Hours per week", "Country"]

data = np.genfromtxt('https://archive.ics.uci.edu/ml/machine-learning-databases/adult/adult.data', delimiter=', ', dtype=str)

Take a look at the data. Let's analyse the labels:

labels = data[:, 14]
np.unique(labels)

array(['<=50K', '>50K'], dtype='<U26')

In order to use it, we need to preprocess the labels to have discrete values:

le= sklearn.preprocessing.LabelEncoder()
le.fit(labels)
labels = le.transform(labels)
class_names = le.classes_

np.unique(labels)

array([0, 1])

Let's remove labels from data and take a look at the data:

data = data[:, :-1]

pd.DataFrame(data, columns=feature_names)

	Age	Workclass	fnlwgt	Education	Education-Num	Marital Status	Occupation	Relationship	Race	Sex	Capital Gain	Capital Loss	Hours per week	Country
0	39	State-gov	77516	Bachelors	13	Never-married	Adm-clerical	Not-in-family	White	Male	2174	0	40	United-States
1	50	Self-emp-not-inc	83311	Bachelors	13	Married-civ-spouse	Exec-managerial	Husband	White	Male	0	0	13	United-States
2	38	Private	215646	HS-grad	9	Divorced	Handlers-cleaners	Not-in-family	White	Male	0	0	40	United-States
3	53	Private	234721	11th	7	Married-civ-spouse	Handlers-cleaners	Husband	Black	Male	0	0	40	United-States
4	28	Private	338409	Bachelors	13	Married-civ-spouse	Prof-specialty	Wife	Black	Female	0	0	40	Cuba
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
32556	27	Private	257302	Assoc-acdm	12	Married-civ-spouse	Tech-support	Wife	White	Female	0	0	38	United-States
32557	40	Private	154374	HS-grad	9	Married-civ-spouse	Machine-op-inspct	Husband	White	Male	0	0	40	United-States
32558	58	Private	151910	HS-grad	9	Widowed	Adm-clerical	Unmarried	White	Female	0	0	40	United-States
32559	22	Private	201490	HS-grad	9	Never-married	Adm-clerical	Own-child	White	Male	0	0	20	United-States
32560	52	Self-emp-inc	287927	HS-grad	9	Married-civ-spouse	Exec-managerial	Wife	White	Female	15024	0	40	United-States

32561 rows × 14 columns

The dataset has many categorical features, which we need to preprocess like we did with the labels before - our explainer (and most classifiers) takes in numerical data, even if the features are categorical. We thus transform all of the string attributes into integers, using sklearn's LabelEncoder. We use a dict to save the correspondence between the integer values and the original strings, so that we can present this later in the explanations.

categorical_features = [1, 3, 5, 6, 7, 8, 9, 13]

categorical_names = {}
for feature in categorical_features:
    le = sklearn.preprocessing.LabelEncoder()
    le.fit(data[:, feature])
    data[:, feature] = le.transform(data[:, feature])
    categorical_names[feature] = le.classes_

data = data.astype(float)

Final look at the preprocessed data:

pd.DataFrame(data, columns=feature_names)

	Age	Workclass	fnlwgt	Education	Education-Num	Marital Status	Occupation	Relationship	Race	Sex	Capital Gain	Capital Loss	Hours per week	Country
0	39.0	7.0	77516.0	9.0	13.0	4.0	1.0	1.0	4.0	1.0	2174.0	0.0	40.0	39.0
1	50.0	6.0	83311.0	9.0	13.0	2.0	4.0	0.0	4.0	1.0	0.0	0.0	13.0	39.0
2	38.0	4.0	215646.0	11.0	9.0	0.0	6.0	1.0	4.0	1.0	0.0	0.0	40.0	39.0
3	53.0	4.0	234721.0	1.0	7.0	2.0	6.0	0.0	2.0	1.0	0.0	0.0	40.0	39.0
4	28.0	4.0	338409.0	9.0	13.0	2.0	10.0	5.0	2.0	0.0	0.0	0.0	40.0	5.0
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
32556	27.0	4.0	257302.0	7.0	12.0	2.0	13.0	5.0	4.0	0.0	0.0	0.0	38.0	39.0
32557	40.0	4.0	154374.0	11.0	9.0	2.0	7.0	0.0	4.0	1.0	0.0	0.0	40.0	39.0
32558	58.0	4.0	151910.0	11.0	9.0	6.0	1.0	4.0	4.0	0.0	0.0	0.0	40.0	39.0
32559	22.0	4.0	201490.0	11.0	9.0	4.0	1.0	3.0	4.0	1.0	0.0	0.0	20.0	39.0
32560	52.0	5.0	287927.0	11.0	9.0	2.0	4.0	5.0	4.0	0.0	15024.0	0.0	40.0	39.0

32561 rows × 14 columns

pd.DataFrame(data, columns=feature_names).describe()

	Age	Workclass	fnlwgt	Education	Education-Num	Marital Status	Occupation	Relationship	Race	Sex	Capital Gain	Capital Loss	Hours per week	Country
count	32561.000000	32561.000000	3.256100e+04	32561.000000	32561.000000	32561.000000	32561.000000	32561.000000	32561.000000	32561.000000	32561.000000	32561.000000	32561.000000	32561.000000
mean	38.581647	3.868892	1.897784e+05	10.298210	10.080679	2.611836	6.572740	1.446362	3.665858	0.669205	1077.648844	87.303830	40.437456	36.718866
std	13.640433	1.455960	1.055500e+05	3.870264	2.572720	1.506222	4.228857	1.606771	0.848806	0.470506	7385.292085	402.960219	12.347429	7.823782
min	17.000000	0.000000	1.228500e+04	0.000000	1.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	1.000000	0.000000
25%	28.000000	4.000000	1.178270e+05	9.000000	9.000000	2.000000	3.000000	0.000000	4.000000	0.000000	0.000000	0.000000	40.000000	39.000000
50%	37.000000	4.000000	1.783560e+05	11.000000	10.000000	2.000000	7.000000	1.000000	4.000000	1.000000	0.000000	0.000000	40.000000	39.000000
75%	48.000000	4.000000	2.370510e+05	12.000000	12.000000	4.000000	10.000000	3.000000	4.000000	1.000000	0.000000	0.000000	45.000000	39.000000
max	90.000000	8.000000	1.484705e+06	15.000000	16.000000	6.000000	14.000000	5.000000	4.000000	1.000000	99999.000000	4356.000000	99.000000	41.000000

As we see, the categorical data has numerical values indicating the categories now.
We now split the data into training and testing:

train, test, labels_train, labels_test = sklearn.model_selection.train_test_split(data, labels, train_size=0.80)

Finally, we use a One-hot encoder, so that the classifier does not take our categorical features as continuous features. We will use this encoder only for the classifier, not for the explainer - and the reason is that the explainer must make sure that a categorical feature only has one value set to True.

from sklearn.compose import ColumnTransformer 
from sklearn.preprocessing import OneHotEncoder

encoder = ColumnTransformer([("OneHot", OneHotEncoder(), categorical_features)], remainder = 'passthrough')

encoder.fit(data)
encoded_train = encoder.transform(train)

We will use gradient boosted trees as the model, using the xgboost package.

import xgboost
gbtree = xgboost.XGBClassifier(n_estimators=300, max_depth=5)
gbtree.fit(encoded_train, labels_train)

XGBClassifier(base_score=None, booster=None, callbacks=None,
              colsample_bylevel=None, colsample_bynode=None,
              colsample_bytree=None, device=None, early_stopping_rounds=None,
              enable_categorical=False, eval_metric=None, feature_types=None,
              gamma=None, grow_policy=None, importance_type=None,
              interaction_constraints=None, learning_rate=None, max_bin=None,
              max_cat_threshold=None, max_cat_to_onehot=None,
              max_delta_step=None, max_depth=5, max_leaves=None,
              min_child_weight=None, missing=nan, monotone_constraints=None,
              multi_strategy=None, n_estimators=300, n_jobs=None,
              num_parallel_tree=None, random_state=None, ...)

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sklearn.metrics.accuracy_score(labels_test, gbtree.predict(encoder.transform(test)))

0.868417012129587

Our predict function, which first transforms the data into the one-hot representation:

predict_fn = lambda x: gbtree.predict_proba(encoder.transform(x)).astype(float)

Explaining predictions

Tabular explainers need a training set. The reason for this is because we compute statistics on each feature (column). If the feature is numerical, we compute the mean and std, and discretize it into quartiles. If the feature is categorical, we compute the frequency of each value. For this tutorial, we'll only look at numerical features.

We use these computed statistics for two things:

• To scale the data, so that we can meaningfully compute distances when the attributes are not on the same scale
• To sample perturbed instances - which we do by sampling from a Normal(0,1), multiplying by the std and adding back the mean.

We now create our explainer. The categorical_features parameter lets it know which features are categorical. The categorical names parameter gives a string representation of each categorical feature's numerical value.

explainer = lime.lime_tabular.LimeTabularExplainer(train, feature_names=feature_names, class_names=class_names,
                                                   categorical_features=categorical_features, 
                                                   categorical_names=categorical_names, kernel_width=3, verbose=True)

We now show a few explanations with a verbose set to True.

np.random.seed(1)
i = 1653
exp = explainer.explain_instance(test[i], predict_fn, num_features=5)
exp.show_in_notebook(show_all=False)

Intercept -0.004040330006700316
Prediction_local [1.03542247]
Right: 0.9999810457229614

exp.as_list()

[('Capital Gain > 0.00', 0.7137120614937713),
 ('Marital Status=Married-civ-spouse', 0.1049685356292349),
 ('Education-Num > 12.00', 0.08327993303179977),
 ('Hours per week > 45.00', 0.07942690191286061),
 ('Age > 48.00', 0.05807536541846803)]

First, note that the row we explained is displayed on the right side, in table format. Since we had the show_all parameter set to false, only the features used in the explanation are displayed.

The "value" column displays the original value for each feature.

The explanations for categorical features are based not only on features, but on feature-value pairs.

LIME has discretized the features in the explanation. This is because we let discretize_continuous=True in the constructor (this is the default). Discretized features make for more intuitive explanations.

As for the values displayed after setting the "verbose" parameter to True: Intercept is the intercept of the linear model used inside the LIME algorithm. Prediction_local is the prediction of this model for the instance of interest, and Right is the xgboost model's prediction for the same instance. We analyse the weights with respect to the intercept.

Note that capital gain has very high weight. This makes sense. Now let's see an example where the prediction is different:

i = 92
exp = explainer.explain_instance(test[i], predict_fn, num_features=5)
exp.show_in_notebook(show_all=False)

Intercept 0.8073078236974233
Prediction_local [0.09965143]
Right: 0.07562913000583649

Let's also analyse one "weird" example. Take a look at the explanations:

i = 18
exp = explainer.explain_instance(test[i], predict_fn, num_features=5)
exp.show_in_notebook(show_all=False)

Intercept 0.1253869743124894
Prediction_local [0.82148369]
Right: 0.005185974761843681

We see that the model predicted the output "<=50K" even though the explanation suggests a different result. Let's do the analysis:
intercept + weights = prediction_local, which is our linear model's prediction, corresponding to label ">50K". The xgboost's prediction is, however, 0.005, so in this case the LIME explainer is not useful.

Homework

• Choose a different model for preparing predictions (you may want to use sklearn models).
• Prepare an explainer.
• Use it on the three instances explained in the tutorial. Did the explanations change? Analyse if the explanations make sense.
• Explain an example where the model prediction was incorrect. Comment on the results.
• Analyse one more example with an interesting explanation.

For the new prediction model I'm choosing random forest with 1000 trees.

from sklearn.ensemble import RandomForestClassifier

rf_clf = RandomForestClassifier(n_estimators=1000)
rf_clf.fit(encoded_train, labels_train)

RandomForestClassifier(n_estimators=1000)

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It predicts only a little bit better, than the previous model: gradient boosted trees

sklearn.metrics.accuracy_score(labels_test, rf_clf.predict(encoder.transform(test)))

0.8615077537233226

There is no need for introducing any changes to the previously defined explainer, cause by its creation the prediction model is not specified. The only new thing needed, is the predict function which has been defined below:

predict_fn_rf = lambda x: rf_clf.predict_proba(encoder.transform(x)).astype(float)

I apply the new prediction model to three preselected examples

i = 1653
exp = explainer.explain_instance(test[i], predict_fn_rf, num_features=5)
print(f"Correct label: {labels_test[i]}")
exp.show_in_notebook(show_all=False)

Intercept 0.060194436622709624
Prediction_local [0.88260848]
Right: 0.997
Correct label: 1

In the first case, we get the same certainty that this sample belongs to the class >50K.
The only difference compared to the previous run, is that the least relevant feature for the previous explanation was the Age, but this explanation has chosen the Relationship.

i = 92
exp = explainer.explain_instance(test[i], predict_fn_rf, num_features=5)
print(f"Correct label: {labels_test[i]}")
exp.show_in_notebook(show_all=False)

Intercept 0.6436302759526994
Prediction_local [0.22404088]
Right: 0.512
Correct label: 0

In the second case random forest has classified the sample wrongly to the class >50K, but the decission wasn't conclusive.
The class <=50K from the explainer is correct and the parameters used for explanation differ only a bit from the previous explanation.

i = 18
exp = explainer.explain_instance(test[i], predict_fn_rf, num_features=5)
print(f"Correct label: {labels_test[i]}")
exp.show_in_notebook(show_all=False)

Intercept 0.18196706838877283
Prediction_local [0.67152889]
Right: 0.12
Correct label: 0

The "weird" example stays weird and the same explanation as before applies this time as well, namely the explainer delivers the score for the sample of 0.67, which puts it into the class >50K, but random forest, which classifies the sample correctly, assigns other class.

i = 7
exp = explainer.explain_instance(test[i], predict_fn_rf, num_features=5)
print(f"Correct label: {labels_test[i]}")
exp.show_in_notebook(show_all=False)

Intercept 0.7273446921010747
Prediction_local [0.24283863]
Right: 0.074
Correct label: 1

In this case both, the original classifier, as well as the explainer, classify the sample wrong. We can see that both approaches are rather certain about the sample belonging to the class <=50K, but actually it belongs to >50K.
Most likely this data sample is an outlier, so the model can't classify it correctly.

i = 61
exp = explainer.explain_instance(test[i], predict_fn_rf, num_features=5)
print(f"Correct label: {labels_test[i]}")
exp.show_in_notebook(show_all=False)

Intercept 0.346098393040719
Prediction_local [0.60526437]
Right: 0.004
Correct label: 0

The last presented sample corresponds with the "weird" example, where the prediction probability clearly shows class <=50K, but the explanation prefers the >50K. The explanation is not useful, because random forest returns score 0.004 which corresponds to the first class, not to the second as the explanation implies based on Predicion_local.

Summary

Even though we need to double check the result of LIME explainer, the majority of tested cased provides helpful interpretation to the inner-works of the model, which would be hard to understand otherwise.